My students are welcome to train with whoever they like. I have even written letters of introduction (at the student's request) if they have a dojo in mind that they wish to visit.
Sometimes dojo-cho can have an unhealthy interest in some of their students' private lives (I have walked away from one organisation because of this). Most Sensei that I know would have no hesitation to say that the more instructors you gain experience of and from, the more rounded one's aikido. Take what suits you and offend no-one by leaving the rest.